The rules, approved by Congress last month, would bar people from 38 mainly European countries from travelling to the United States without a visa if they have visited Iran, Iraq, Syria or Sudan since 2011.
Dual nationals of those countries would also be banned from using the Visa Waiver Program (VWP).
"Recently some US representatives have put some plans together which can only be referred to as harassment," parliament speaker Ali Larijani told lawmakers.
"If they don't amend it, there will be reciprocation from the Iranian side."
The US plan came after calls from lawmakers and authorities to reduce security vulnerabilities after November's deadly jihadist attacks in Paris.
Some of the attackers were French and Belgians who could have travelled unrestricted to the United States.
Iran recently consulted with European countries and said the visa plan went against the spirit of the July 14 deal struck with world powers led by the United States over Tehran's nuclear programme.
European diplomats have also warned of potential retaliation for the measures, arguing that the visa programme is based on reciprocity.
The president of the French Senate, Gerard Larcher, criticised the US plans on a visit to Tehran last month, saying they sent the "wrong signal" and undermined efforts to build confidence with Iran.
Those affected would not be barred from the United States but would be required to obtain a visa through standard means, which includes a face-to-face interview at a US consulate.
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